Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=200005;
int n,i,a[N],f,t,pt[N];
int main()
{
	scanf("%d",&n);
	for(i=1;i<=n;++i)
	{
		scanf("%d",a+i);
		pt[a[i]]=i;
	}
	for(i=n-1;i>=1&&pt[i]<pt[i+1];--i);
	if(i<1)
	{
		printf("0");
		return 0;
	}
	t=1,f=i+1;
	for(--i;i>=1;--i)
	{
		if(pt[i]<pt[f]&&pt[f]<pt[i+1]||pt[i+1]<pt[i]&&pt[i]<pt[f]||pt[f]<pt[i+1]&&pt[i+1]<pt[i])
		{
			++t;
			f=i+1;
		}
	}
	printf("%d",t);
	return 0;
}